1,356,333 research outputs found
A comparison among various notions of viscosity solution for Hamilton–Jacobi equations on networks
No full textThree definitions of viscosity solutions for Hamilton–Jacobi equations on networks recently appeared in literature (Achdou et al. (2013) [1], Imbert et al. (2013) [4], Schieborn and Camilli (2013) [6]). Being motivated by various applications, they appear to be considerably different. The aim of this note is to establish their equivalence
A System of Hamilton-Jacobi Equations Characterizing Geodesic Centroidal Tessellations
No full textWe introduce a class of systems of Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, i.e., tessellations of domains with respect to geodesic distances where generators and centroids coincide. Typical examples are given by geodesic centroidal Voronoi tessellations and geodesic centroidal power diagrams. An appropriate version of the Fast Marching method on unstructured grids allows computing the solution of the Hamilton-Jacobi system and, therefore, the associated tessellations. We propose various numerical examples to illustrate the features of the technique
A System of Hamilton-Jacobi Equations Characterizing Geodesic Centroidal Tessellations
No full textWe introduce a class of systems of Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, i.e., tessellations of domains with respect to geodesic distances where generators and centroids coincide. Typical examples are given by geodesic centroidal Voronoi tessellations and geodesic centroidal power diagrams. An appropriate version of the Fast Marching method on unstructured grids allows computing the solution of the Hamilton-Jacobi system and, therefore, the associated tessellations. We propose various numerical examples to illustrate the features of the technique
Formal verification problems in a big data world : towards a mighty synergy
No full textFormal verification requires high performance data processing software for extracting knowledge from the unprecedented amount of data coming from analyzed systems. Since cloud based computing resources have became easily accessible, there is an opportunity for verification techniques and tools to undergo a deep technological transition to exploit the new available architectures. This has created an increasing interest in parallelizing and distributing verification techniques. In this paper we introduce a distributed approach which exploits techniques typically used by the bigdata community to enable verification of very complex systems using bigdata approaches and cloud computing facilities
A mathematical framework unifying various Shape from Shading approaches
No full textInternational audienceBy slightly modifying the notion of singular viscosity solutions [Ishii-Ramaswamy:95,Camilli-Siconolfi:99,Camilli:01,Camilli-Siconolfi:02] we define a new mathematical framework allowing to unify the various theoretical results proposed in the Shape from shading literature. We demonstrate the existence and the uniqueness of the new solution for a class of Hamilton-Jacobi equations including the classical Shape-From-Shading equations [Prados-Faugeras:03], in a bounded locally Lipschitz domain. Some stability results are proved. Finally, we propose a provably convergent numerical method for approximating the solution and we demonstrate its relevance and its efficiency by numerical experiments on real images
A policy iteration method for mean field games
No full textThe policy iteration method is a classical algorithm for solving optimal control problems. We introduce a policy iteration method for Mean Field Games systems and we prove, under a classical monotonicity assumption on the coupling cost, the convergence of this procedure to the solution of the problem
Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative
No full textWe study existence, uniqueness and regularity properties of classical solutions to viscous Hamilton–Jacobi equations with Caputo time-fractional derivative. Our study relies on a combination of a gradient bound for the time-fractional Hamilton–Jacobi equation obtained via nonlinear adjoint method and sharp estimates in Sobolev and Hölder spaces for the corresponding linear problem
A policy iteration method for mean field games
No full textThe policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of the problem. We also introduce suitable discretizations to numerically solve both stationary and evolutive problems. We show the convergence of the policy iteration method for the discrete problem and we study the performance of the proposed algorithm on some examples in dimension one and two
A quadratic mean field games model for the langevin equation
No full textWe consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. An appropriate change of variables transforms the Mean Field Games system into a system of two coupled kinetic Fokker–Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system
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